Wednesday, May 17, 2006

Jim Snapp on Census Numbers

I've received the following essay from Jim Snapp on the subject of the large numbers of Israelites recorded especially in the book of Numbers. He proposes a reduction in the numbers of MT. Although this is a thesis with which I strongly disagree, I'm sure it will provoke discussion on what is one of my favourite topics ...

What follows is from Snapp.

The Quest for the Historical Censusby James Snapp, Jr.

I usually don’t engage in Old Testament textual criticism—partly because I am spectacularly incompetent at Hebrew. And I usually avoid situations in which the slightest possibility of having to do anything mathematical exists. But some time ago, I attempted to resolve the problem of the large numbers of the Hebrew population of the exodus, by way of conjectural emendation. This essay explains my solutions.

The census numbers of the exodus have been approached mainly in four ways:(1) Deny all or almost all historicity of the censuses—implying that the text is fictitious.(2) Accept the extant text as it stands—implying that the early Hebrew nation consisted of over 600,000 men and their families.(3) Maintain that the census-figures have a historical core at some point in the history of Israel, but the text has been drastically misplaced by redactors.(4) Regard the census-numbers as a problem which textual analysis can solve—implying that the extant text is not the original text.

All four views have their weaknesses. My intention here is to demonstrate the cogency of the fourth position and show how textual analysis can resolve the problem.

"What problem?" you ask. Well, the numbers are just too big! The birthrate which would be required for c. 75 Hebrews to become a nation of 600,000 men and their families in 430 years (depending on which text-base one follows) would be not just remarkable; it would be astronomically greater than the birthrate of any civilization in antiquity. Also, a population of 600,000 men would tend to leave behind more evidence of a sojourn in Transjordan than has been archaeologically confirmed. Plus, some problems appear when one attempts to interlock this large amount with other factors in the Bible (such as the Hebrews’ difficulty in conquering the Amalekites).

George Mendenhall—if I understand his theory—has proposed that the Hebrew word for "thousands" in the census-lists actually means "recruiting district" or "squad." Thus Numbers 1:21’s description of the militia from the tribe of Judah—"forty-six thousand and five hundred" —ought to be understood to describe 46 squads of men, whose total number was 500. Applied to the entire first census, this yields a total of 598 squads, numbering a total of 5,550 men in the militia.

There are some difficulties with Mendenhall’s idea.

First, it seems strange that anyone should make an exact count of squads and an inexact count of troops.

Second, a population of about 22,000 would no longer exist after the plagues described in Numbers 16:49 (in which 14,700 died—and the militia is not in view) and Numbers 25:9 (in which 24,000 people died—and which Paul affirms as "23,000 in one day" in 1 Corinthians 10:8).

Third, Numbers 3:42-43 lists the number of "firstborn sons" as 22,373; unamended, this cannot be reconciled with a total militia of about the same number.

Fourth, passages such as Exodus 18:25, Numbers 22:3-5, and Numbers 23:10 indicate that the Hebrew nation’s size was indeed considerable.

Fifth, such a hypothesis posits squads of varying size: an average size of 11 for Dan, 7.5 for Naphthali, and 5 for Simeon. Such a census seems pointless, as if someone would count their arrows and quivers but not be concerned about the number of arrows in any given quiver. It is difficult to see the point of a "squad" statistic which does not represent a certain number of men.For further examination of Mendenhall’s proposal see pages 129-134 of Gleason Archer’s Encyclopedia of Biblical Difficulties, in which Archer supports the extant text.

John Wenham has made a similar proposal, in which the Hebrew term is understood to refer to a full-time soldier. A fine summary of his view is contained in Eerdman’s Concise Bible Handbook in his article "The Large Numbers of the Old Testament," pp. 79-81. He points out (as other have) that Gen. 36:15 and Ex. 15:15 use a similar term to refer to "chieftains" of Edom, and theorizes that in paleo-Hebrew consonantal script the terms were not readily distinguishable. Wenham thinks that the extant text is the result of a conflation of a once-separated listing of chieftains and thousands.

In the extant text, Simeon has 59,300 men. Wenham suggests that this originally described 57 armed men and 23 hundreds, which was written down as "57 ’lp; 2 ’lp 3 ‘hundreds.’" The two ’lp-units were then combined by a later copyist, yielding the reading 59 ’lp 300 in the extant text. Wenham concludes that "The total fighting force is some 18,000, which would probably mean a figure of about 72,000 for the whole migration." He also proposes that the figures for the Levites have been corrupted by being multiplied by a factor of ten (thus the tribe of Levi totalled 2,200 men, not 22,000).

I agree that the census-lists of Numbers originally contained a delineation of full-time officers along with the number of militia-members. Wenham is on the right track. (Also, the chiastic structure of Exodus 15:15 favors the idea that in the Pentateuch, ’lph never refers to "recruiting districts," although such a usage of the word is feasible in passages such as Judges 6:15 and Micah 5:2.)

However, Wenham’s numbers still seem small—for some of the same reasons why Mendenhall’s reconstruction seems small, but also because it is difficult to see how a "total fighting force" of 18,000 apparently includes, in Joshua 4:13, 40,000. It is also difficult to see how Exodus 12:37 could describe a population of about 72,000 as "about six hundred thousand on foot that were men, besides children," and how Moses could assert the same thing in Numbers 11:21 ("The people, among whom I am, are six hundred thousand footmen").

Borrowing Wenham’s idea and re-applying it, and combining it with some ideas of my own, let us re-examine the census-numbers and some related texts.

The first texts under consideration are Exodus 12:37 and Numbers 11:21, where the extant text yields "600,000." I propose that this reading is a corruption by copyists. The original reading is "60,000" in both cases. Since the case for this smaller number as the original text depends somewhat on material in other parts of the hypothesis, I will present those other parts first, and then argue for this reading and explain how it may have originated. For now, I only note that the shift from "60,000" to "600,000" would be a very simple shift to make in paleo-Hebrew script.

The second text is Numbers 1:20-46 (more precisely, the numerals within that passage. I propose that this passage was based on a source which originally tallied the number of men in the Hebrew militia 13 months after the exodus. The original source, though, did not consist of merely "thousands" and "hundreds" (plus the occasional tens-unit). The original census-list consisted of a list of officers (or "chiefs"), and thousands, and hundreds. However, the written word for "chief" was indistinguishable from the word for "thousand." So one might imagine something like the following scenario:

Imagine a list that is written to keep track of the size of a small army composed of three divisions, led by three generals named Moe, Larry, and Curly. In the language of Moe, Larry, and Curly, the word "elf" can mean "officers" and it can also mean "thousand." (It can even mean "oxen" sometimes.) The three generals want their list to keep track of how many officers they have, and how many non-officers they have. So their original list looks like this:

But then along comes a copyist who does not discern that one group of Elf is officers and the other group of Elf is thousands. He thinks they’re both thousands-units, and—out of a sense of tidiness—combines them. The result looks like this:

I submit, following Wenham, that the census-numbers went through the same sort of conflation. I favor a different calculation, however. Here is a comparison of the extant text to a hypothetical reconstruction of the original numbers in the census in Numbers 1:20-26. The extant text is in normal print; the conjectural emendation is underlined. The "alph." stands for chiefs and the "elph" stands for thousands.

The third text is Numbers 2:3-32 (more precisely, the numerals in that passage), in which the militia-population of the individual tribes are given in the encampment-array. The exact same numbers are given here that were given in the census in chapter one, because they were affected by the same mis-combination. Originally the listings here consisted of officers + thousands + hundreds (plus 50 for Gad).

So in Numbers 2:9, the extant sub-total of 186,400 was originally "168 officers, with 18,400 non-officers." 2:16, 2:24, and 2:31 may be reduced to their original numbers along the same lines.

The fourth text is Numbers 3:11-50 (more precisely, the numerals in that passage), in which a census is taken of the Levites clan-by-clan (with three clans: Gershonites, Kohathites, and Merarites). I propose that the census-numbers here were also corrupted, but in a more ordinary way than the numbers of the military censuses. The numbers were multiplied by ten.Here is a comparison of the extant text with the conjectural emendation:

This implies that the 22,273 firstborn non-Levite Hebrew males described in Numbers 3:43 were exchanged for 2,200 Levites. One Levite was considered exchangeable for 10 non-Levites (the tithe-ratio). Thus the text originally stated that 2,200 Levites were exchanged for 22,000 non-Levites. This left 273 firstborn sons unexchanged, and this is why they needed to pay 5 shekels each in Numbers 3:45-51 (totaling 1,365 shekels in Numbers 3:50).

The variant in 3:28 requires special attention: was it originally 860 or 830? (And, in the corrupted copies, was it 8,600 or 8,300?) The total is supposed to be 2,200 (or, in the extant text, 22,000). But 750 + 860 + 620 = 2,230, not 2,300 (and, in the extant text, 7,500 + 8,600 + 6,200 = 22,300, not 22,000). The reading "8,600" is the more difficult reading, and it is also the standard Hebrew reading (though some Septuagint manuscripts read "8,300"). But it makes the total add up to 2,230 (or, 22,300). How does one explain this?

One way is to propose that it was simply miscopied, and subsequent Hebrew copyists mechanically copied the erroneous number. Another explanation is a fairly ancient tradition-story (which assumes the authenticity of the extant text): the extra 300 were first-born sons themselves, and therefore could not redeem the non-Hebrew firstborn.

I suspect that "8,600" is a copyist’s error (in addition to the error of multiplying the Levite-clans’ population by ten) and that the tradition-story was created to explain it. But either reading can be adopted with no effect on the conjectural emendations (though, as with the extant text, to propose that the extra 300 or extra 30 is original leaves one with the question of why such a thing was not explicitly explained somewhere in the text).

The fifth text is Numbers 4:34-49, where the Levites age 30-50 are counted clan by clan. Again, I propose that a copyist mistakenly multiplied the numbers by ten. Here is a comparison of the extant text and the conjectural emendation:

Adding to the plausibility of this theory is a point of practicality: the reconstructed text implied that there were fewer men ministering at the tabernacle. It is difficult to see how, with the higher amounts, every adult Levite had something to do.

Now let’s return to the "60,000" at Exodus 12:37 and Numbers 11:21. The reconstructed total of the first military census = 54,100 soldiers.

The reconstructed total of the census of Levites age 30-50 = 858. Considering that there were 2,200 Levite males in all, we can fairly propose that about 300 of them were between age 20-30. We can also fairly propose that approximately 200 of them were over age 50. Now consider the total number of adult Hebrew males that this generates:

54,100 + 858 + 300 + 200 = 55,458.

55,458 is close to 60,000. Thus the re-structured census-figures harmonize with the reconstructed "60,000" in Exodus 12:37 and Numbers 11:21.

The sixth text is Numbers 26:1-51 (more precisely, the numerals within that passage), the second Hebrew military census. Here is the reconstruction:

EXTANT:……………………ORIGINAL:

REUBEN: 43,730…………40 alph 3 elph 7 m. + 30

SIMEON: 22,200…………20 alph 2 elph 2 m.

GAD: 40,500………………37 alph 3 elph 5 m.

JUDAH: 76,500……………71 alph 5 elph 5 m.

ISSACHAR: 64,300………61 alph 3 elph 3 m.

ZEBULUN: 60,500………57 alph 3 elph 5 m.

MANASSEH: 52,700……48 alph 4 elph 7 m.

EPHRAIM: 32,500………30 alph 2 elph 5 m.

BENJAMIN: 45,600………43 alph 2 elph 6 m.

DAN: 64,400………………61 alph 3 elph 4 m.

ASHER: 53,400……………50 alph 3 elph 4 m.

NAPHTHALI: 45,400……42 alph 3 elph 4 m.

TOTAL: 601,730…………560 alph + 41 elph + 7 m. + 30

Actual total of soldiers: 42,290

The seventh text is Numbers 26:62. I propose that this amount has been multiplied by ten: "23,000" in the extant text represents an original 2,300 Levites. If 1,000 Levites (out of a total of 2,300] were over age 20, then the total adult male Hebrew population at the second census was about 43,290 men.

A note about the implications of these reconstructed numbers: the Hebrews would leave Egypt numbering 55,458 men and enter the Promised Land with about 43,290 men – a net loss of about 12,168 men (I am using precise numbers here, but treat them as estimates). Give each man a wife and two kids, and this means that about 221,832 Hebrews left Egypt, and about 173,160 entered the Promised Land – a net loss of 48,672.

The eighth text is Exodus 38:21-30, especially verses 25-28. This passage as a whole may be considered part of "Ithamar’s Ledger," an independent piece of source-material which tallied the offerings given in chapter 35 and noted how they were used. Verses 25-28 seems question-raising: the tabernacle was finished and inaugurated on the first day of the first month of the second year after the exodus (Exodus 40:17), and the census did not take place until the first day of the second month of the second year after the exodus (Numbers 1:1-2). How was it possible for the silver bekahs that were collected in the census to be among the items used to make the tabernacle?

This can be accounted for in the following speculative way: originally, Ithamar’s Ledger included a list of the gold, silver, and bronze that had been collected in chapter 35, with no mention of the silver bekahs collected in the census. However, Ithamar’s Ledger was damaged and the information about the silver offering was lost. A copyist/redactor filled in the gap by supplying material from another source (possibly a different part of Ithamar’s Ledger) that noted the total amount of money given in the census. Originally this supplement went,

"The silver obtained from those of the community who were counted in the census, one bekah per person, was 275 shekels from officers and 26,775 shekels from everyone who had crossed over to those counted, 20 years or more ~ a total of 550 officers, 53 thousand and five hundred and 50 men."

The "275 from officers," however, was misunderstood to mean "275 thousands," and this was combined with the 26,775, yielding a combined total of 301,775 shekels. The closing tally of officers and thousands was also misunderstood and was combined into one unit of thousands only (with the resultant reading, "603 thousands and five hundred and fifty men"). Possibly, having "550" at both the beginning and end of the number contributed to a copyist’s misunderstanding.

A later copyist, noting that this implied that just over 100 talents had been collected (reckoning that 1 talent = 3,000 shekels), and also noting that the tabernacle had 100 bases, entered a speculation that the (apparently existing) 100 talents of silver were used to make 100 bases, and that the leftover 1,775 silver shekels were used for other purposes. In other words, verse 27 is a late interpolation.

The text was also supplemented by a note that the shekel being used was the "sanctuary shekel." And thus the text reached its extant form. It should be emphasized that the text as it stands merely reports the contents of Ithamar’s Ledger, without necessarily endorsing its contents.

The ninth text is Numbers 31:32-47, a description of the spoils of the Hebrews’ military campaign against the Midianites. According to the extant text, the Hebrews were phenomenally successful: 12,000 men (a thousand from each tribe, as 31:5 says) brought back the following plunder:

These numbers, though large, are not altogether impossible. However, these numbers probably represent an original text in which the numbers were smaller by a factor of twenty. (If the extant text of Numbers 31:32-47 is not corrupted, and the extant text of the censuses is corrupted (as theorized), then prior to entering the Promised Land, the Hebrew population (173,160) absorbed a population of Midianite virgins (32,000) with the result that about 1 in 6 individuals in the encampment was a Midianite woman. That doesn't sound right to me.)

If a copyist erroneously multiplied the numerals here by 20, then the original text had the following amounts in 31:36-40:

And the original over-all distribution-proportion to the Levites was not 1 part out of 500, but 1 part out of 25. (The extant text's record of the Levites' share is thus correct.)

The numbers for the sheep, cattle, donkeys, and virgins were erroneously multiplied by 20 by an early copyist, who also wrote the paleo-Hebrew equivalent of "500" instead of "25" in 31:28 (i.e., he multiplied the number 25 by 20, also). Even though there's no manuscript-evidence to support the idea that the numbers for sheep, cattle, donkeys, and virgins were multiplied by 20 by an early copyist, and that at some point the original "1-in-25" was replaced by "1-in-500," (which is also a multiplication by 20), I think this hypothesis makes a lot of sense. When all the numbers in this passage are reduced by a factor of 20, the resultant numbers look pretty plausible.

The tenth text to consider is Joshua 4:13. The extant reading of this verse is correct. But the usual interpretation of this verse is incorrect. Usually it is understood to mean that about 40,000 men from the tribes of Reuben, Gad, and Manasseh crossed over the Jordan River.That is somewhat problematic for the extant text, since the total number of men from the tribes of Reuben, Gad, and Manasseh in the extant text of the second census is 136,930—more than three times 40,000. At first glance, it may also seem problematic for the reconstructed text, in which the total population of these three tribes in the second census is only 11,056.

This is resolved when one realizes that the 40,000 in Joshua 4:13 is not describing the Transjordan tribes; it is describing the total number of soldiers who crossed the Jordan. In other words, Joshua 4:13 is part of the closing parentheses of the account of the crossing, not a detail about the number of troops from the Transjordan tribes (who were supposed to go across "all of you," "every man," according to Numbers 32:20ff.).

When "about 40,000" is seen as the total number of individuals in the Hebrew militia, a remarkable harmony with the reconstructed original text of the second military census may be seen: the total number of soldiers in the reconstructed text of Numbers 26:1-51 is 42,290. This could readily be described as "about 40,000," especially if some men remained to guard the women and children in the Transjordan territory (which seems to be suggested in Joshua 22:8).Notice the harmony between the (unmultiplied) 60,000 of Exodus 12:37 and the (unmiscombined) 55,458 of the first censuses (militia + adult Levite males). Also notice the harmony between the (unmiscombined) 42,290 of the second military census and the (extant, uncorrupted) 40,000 of Joshua 4:13. The harmony of these numbers suggests that these hypotheses, or something fairly close to them, reflect the original text and its transmission-history.

In addition to these ten passages, one may consider the various instances elsewhere in which a difficulty is readily explained by positing a misunderstanding of the Hebrew term for "officer." John Wenham has noted some of these points previously.

Judges 12:6 refers to 42 officers, not 42,000 soldiers. Judges 20:2 describes 400 officers, not 400,000 soldiers. Similarly in Judges 20 the scenario is remarkably clarified when one realizes that the Benjamite force consisted of 26 sword-wielding officers (not 26,000 soldiers) with 700 sling-wielding volunteers, and that they kill, in subsequent days of battle, 22 officers, and then 18 officers, and then about 30 men (in Judges 20:21, 20:25, and 20:31. Notice that the third amount is seen to indicate to the Benjamites that they are defeating their opponents as they were on the previous days, in 20:32. 20:35 and 20:46 originally meant that 25 Benjamite officers and 100 slingers were killed, leaving 600, not 1,600, whose escape is described in 20:47.And in First Samuel 6:19, God did not strike down 50,070 men at Beth-shemesh; a much more likely reading of the text is "70 men and 50 cattle of a man" as noted in the footnote here in the NKJV—"’eleph" being rarely used to refer to cattle. Other passages (such as First Samuel 13:5 and First Kings 4:26 ~ compare this to Second Chronicles 9:25) indicate that copyists sometimes multiplied numbers by 10. I bring up these passages to show that the misunderstanding of ’lph and the multiplication of some numbers by ten were not limited to the censuses. This may augment the plausibility of the hypothesis.

I wish to mention one further text, or rather, two parallel-texts, in Ezra and Nehemiah. In regard to these texts, the interesting feature is not so much a text-critical point as a point of interpretation (which may stand or fall separate from all the rest of this) suggested by the conjecture thus far.

Notice that the reconstructed total of the Second Census is 42,290. While that reflects the militia-size, two other groups are also counted: the Levites, and the 70 elders (referred to in Exodus 24:1 and Numbers 11:16-30). If one ignores the Levites, and adds together the militia and the elders, one arrives at a total of 42,360. In Ezra 2:64 and Nehemiah 7:66, this same number, 42,360, happens to be the total number of Israelite males returning to Judah after the Exile. In Ezra and Nehemiah, this number is at the end of a detailed listing of returning Israelites. In Ezra, if one adds up the actual total of the list, the sum is 29,818. In Nehemiah, the sum is 31,089.

In Nehemiah, the list begins with a list of 12 leaders of those who returned. This roughly parallels the twelvefold arrangement of the censuses in Numbers. Also, the list is accompanied by a list of offerings of gold, silver, and clothing—another rough parallel to Numbers.If the reconstruction is correct, and if a text containing it was known to the author of the lists which were the basis for Ezra 2:2-70 and Nehemiah 7:5-73, that author may have intended to show that the community of God’s people who re-entered the Promised Land after the Exile, in the days of the high priest Joshua son of Azaniah, were fulfilling the role of the Israelites who had originally entered the Promised Land in the days of Joshua son of Nun.

The lists in Ezra and Nehemiah may have been deliberately structured, via statistical selection, to yield a total congruent to the number of Hebrew militia-members and elders who originally entered the Promised Land. Josephus (Antiquities of the Jews, book 11, ch. 3, para. 10) states that the populace returning from the Exile was counted "above the age of 12 years." Josephus is not very reliable in this particular section (see Addendum). But if in fact the population was counted from age 12 and up, it could be because the list-composer realized that by doing so, the total population-numbers of his list would be somewhat synchronous with the population-numbers of the original Hebrew entrants into the Promised Land as it appeared in his copy of Numbers.

Such a history-repeating point would be at home in Ezra-Nehemiah, since in Nehemiah 9-10, Ezra’s generation is called upon to re-affirm the covenant of Moses, as was done by the first generation of Hebrews who had entered the Promised Land. Nehemiah 10:32 contains another example of a post-Exile action based on the pattern of the censuses in Numbers (the sanctuary-tax).

So, I think a reconstruction of the numbers in the text along the lines I have proposed is a good working hypothesis. It may contribute to a more accurate perception of the size of the Hebrew population in the days of Moses and Joshua. It may suggest steps in the transmission of the text. And perhaps it may indicate some sort of thematic relationship between the original text of the Second Census and the 42,360 in Ezra-Nehemiah.

ADDENDUMNow that I have mentioned the reference in Josephus (Antiquities of the Jews, book 11, ch. 3, para. 10), I suppose it might be worthwhile to comment on a little tangent therein. Josephus states that the total number of people returning from the Exile was "four hundred and sixty-two myriads and eight thousand." Since a "myriad" = 10,000, Josephus’ number = 4,628,000. That is obviously not right. But Josephus goes on to list some numbers that are in agreement with the Biblical text:

Josephus: the Levites were 74.Ezra 2:40: the Levites: the sons of Jeshua and Kadmiel, 74.Nehemiah 7:43: the Levites: the sons of Jeshua and Kadmiel, and of the sons of Hodevah, 74.

Josephus: singers of the Levites, 128.Ezra 2:41: the singers: the sons of Asaph, 128.Nehemiah 7:44: the singers: the sons of Asaph, 148.

Josephus: … and of the sacred ministers 392.Ezra 2:58: All the Nethinim and the children of Solomon’s servants were 392.Neh. 7:60: All the Nethinim and the sons of Solomon’s servants were 392.

(Note: since Nehemiah only says, describing his list, words to the effect that "This is the list that I found," and does not vouch for its accuracy, I see no apologetic impetus to seek to harmonize his list with Ezra’s.)

Josephus also states that "The number of women and children mixed together was 40,742," which would interlock feasibly with a male population over 12 years of age equaling 42,360—but it does not interlock with a male population over 12 years of age equaling 4,628,000! Josephus, it seems, was either working with a corrupted text, or was terribly misunderstanding a text. But what sort of textual corruption or misunderstanding could produce 4,628,000 from a text which originally read 42,360?

I conjecture that Josephus was working with a poorly-copied text of Ezra-Nehemiah which included the Nethinim-listing twice—once as "Nethinim," and once as "officers" — perhaps as the result of the insertion of a marginal note that Nethinim were officers—not military officers, but officiators at the temple. And the word used for "officers" was ’lph.

This was (densely) understood to mean that there were 392 Nethinim, and 392,000 temple-officers. Since it was obvious (even to the dense copyist) that the temple-officers could not outnumber the rest of the population, the copyist fixed that discrepancy by increasing the population-total by a multiple of 100, thus changing the original "42,360" to "4,236,000." Thus, by adding 4,236,000 to 392,000, the copyist came up with a fresh total of 4,628,000—which is exactly what we read in Josephus.

9 comments
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Excellent treatise, Jim. It seems to clear up a lot of inconsistencies, and serves the purpose of conjectural emendation:When the text CAN'T be right as it is, come up with what it MIGHT have been that IS right.

But . . . JS:And in First Samuel 6:19, a much more likely reading of the text is "70 men and 50 cattle of a man" as noted in the footnote here in the NKJV—"’eleph" being rarely used to refer to cattle.

MT:19 "And He smote of the humans of Beth-Shemesh because they looked in the ark of YHWH, and He smote of the community: seven-tens men; five-tens ALP men. And lamented the community because YHWH struck of the community with a huge strike."

I personally believe that the children of Israel were only in Egypt about 225 years (the 430 years was from the promise given to Abraham in Genesis ~15 till the Exodus - Gal. 3:17, and Exodus only records 4 generations between Jacob and Moses).

But even taking this 225 year figure for the stay in Egypt and using quite conservative birth-rates, the figures easily come out at 600,000 men by the Exodus:

1. 225 years allows 7 generations (30 years per generation).

2. Each man had, on average, 4 sons (this is the average for Jacob's sons, and was presumably even higher during the period when it is specifically noted that they multiplied exceedingly - Ex. 1:7, 12, 20).

3. The generational totals are: Starting-point: 46 grandsons of Jacob entered Egypt (1) 184 great-grandsons after 30 years, (2) 736 g-g-grandsons after 60 years, (3) 2944 g-g-g-grandsons after 90 years, (4) 11776 g-g-g-g-grandsons after 120 years, (5) 47104 g-g-g-g-g-grandsons after 150 years, (6)188416 g-g-g-g-g-g-grandsons after 180 years, (7) 753664 g-g-g-g-g-g-g-grandsons after 210 years.

Subtract from this last figure the first five/six generations (who had died by the Exodus): (46 + 184 + 736 + 2944 + 11776 + 47104 = 62790), and you are still left with nearly 700000 men.

There are several problems apparently solved, the chiefest of which are:

1) the number of firstborn doesn't square with the number of Levites

2) The number who crossed over in Joshua 4:13 is too low to represent the 2½ tribes

3) The archaological record should reveal at least a couple million naturally-mummified corpses buried along the track of the Exodus, but none have been found.

Furthermore, I would add that the numbers are a bit too rounded off to resist the urge to reduce them by a factor of ten or more. The mere fact that it CAN be done implies that it SHOULD.

For what it's worth, the 30 year generation approach seems to overlook a basic factor: for each succeeding generation, the spread within that generation widens. Whilst Moses was only 4 generations removed from Jacob, Joshua was about 7 generations below him. Thus many of Levi's descendants of the 5th, 6th, and 7th generation had not yet been born as of the Exodus.

Nevertheless, the compounding power of procreation can easily be underestimated. Only 25 male Mayflower passengers passed on their genes to posterity (and only 7 females), yet 210 years later, in 1830, probably the better part of the US population of over 12 million was descended from at least one of them.

I did a bit of work on the same subject, but my method of solving the problem rests in seeing a multiplication of almost all the original numbers in the OT texts by a factor of 10 or 100, in order to raise the various numbers up to something "respectable" dating to sometime in the late Persian period.

Other works similarly trying to reduce the numbers include those by David Fouts (Dallas doctorate. Not sure if it's published. He's now at Bryan College); Colin Humphreys (Prof. of Materials Science in Cambridge) in Vetus Testamentum with a reply by Milgrom; I think there is also some work to this effect by Uwe Zerbst in German. It might be in his response to Finkelstein.

DRB -- Your note about I Sam. 6:19 (a passage which was noted tangentially in the essay) is well-taken. The text seems capable of meaning "70 commoners and 50 chief men." On the other hand, Gleason mentions (Encyclop. Of Bible Difficulties, p. 169) that Josephus (Antiquities 6:1:4) mentions only the loss of 70 men, not 120. I don’t see why the author would have made a distinction between chiefs and non-chiefs instead of just mentioning the total number of the slain.

The 50 slain oxen -- assuming that there were 50 slain oxen -- were simply in the wrong place at the wrong time. It doesn’t seem much of a stretch at all to picture a herd of 50 oxen near the fields of a rich citizen.

Andrew W -- I’m no kind of specialist in the study of birth-rates; I am confident however that if a specialist in ancient Egypt and a specialist in birth-rates got together and sorted through the evidence, they would conclude that the existence of a population of over 1,000,000 Hebrew slaves in Egypt at any timein antiquity, rising from 75 ancestors in 430 years or less, is implausible. I know this question is important since the answer creates (or erodes) a large part of the impetus for the investigation; nevertheless it may be a question for another venue since it’s not about textual criticism.

KPE -- Great work and very thorough; you’ve saved me the trouble of writing a sequel. I agree with very many of your points about copyists' simple multiplication-errors. And I noticed that we both have said similar things about the report about the silver in Ithamar’s ledger. But although positing simple multiplication-errors resolves many peripheral issues, my main subject -- the census-numbers -- doesn’t seem to be capable of that solution; the precision of some numbers (603,550, for instance), and the careful comparison of some numbers with others, suggests that some other mechanism is at work also. (And, thanks for pointing out the reference to "40 thousand" in Judges 5:8; if this is a non-multiplied number, it tends to affirm that the approx. 40,000 mentioned back in Joshua 4:13 = all the Hebrew males eligible for military service.)

KPE:"all are simply the result of multiplication by 100 or by 10, with only a very fewexceptions (namely, Ex 38.25-28 and Num 3.43)."

I address these passages separately below.Question: by what mechanism would a Multiplier go about changing that many numbers scattered across half the Hebrew Bible? It's not so simple a matter as squeezing in an extra zero or two at the end and adding a comma.

Also, the numbers of Job's estate in Job 1 and 42 equally beg reduction* by 90% (other than his 1 wife, 7 sons, and 3 daughters); did the Multiplier's work here leave no trace?

*still leaving Job with twice the number of oxen to lose in one fell swoop as those "of a man," which are calculated to have fatally crowded around the ark in Judges 6:19--thus lending credence to Jim's hypothesis.

KPE:"Note also that the total of 493 firstborn (roughly 8% or one out of twelve) of 6,035men, is a more realistic ratio for firstborn males than is 22,273 (roughly 4% or one outof twenty-five) out of 603,550."

Both numbers are still inconceivably large. I took a census of a sex-parity community of 84 people (8 of them childbearing women) with an average of 5 unmarried children per father, and the total ratio of firstborn sons to non-firstborn sons was only 1 to 3. Each mother in the entire range of child-bearing age would need to have NINE more sons just to bring the ratio down to 1 to 7, and several of those already have six sons and are unlikely to have any more. If each firstborn son had even 12 living brothers, .6 million men in 215 years is a minimum result. Because everyone in the tribe had to also average 13 corresponding daughters for all those sons to marry.

KPE:"My suggestion would be that the original of the silver section lacked mention of the census and the talent per base equation, and that the total number of talents and shekels of silver was originally different."

But note that in this passage (back as far as v. 24), totals are given in talents and shekels, indicating at least that a different Multiplier was at work. Furthermore, the NRSV missed an important numeral in the sum of v.25: it begins with 100 shekels.

KPE:"Note also that the census in the narrative has still not yet taken place, so that its mention in 38.25-26 is peculiar."

Certainly it is, but there is no evidence that Moses wrote Exodus 38 in a different timeframe than he wrote Numbers 1, so even the charge of anachronism fails here.

One thing to keep in mind is that Exodus records non-Israelites leaving with the Hebrews. It's not clear to me if the 600,000 figure is intended to include them or not. It's plausible as far as I can tell that this figure is supposed to include all who could fight, including the non-Israelites. That would at least mitigate the argument that over a million Hebrews slaves wouldn't have been left out of the history books. Of course, given the tendency of Egyptians not to write about their failures it would make sense not to write about the Hebrews at all.

Installing Minecraft Forge and ComputerCraft
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The occasion for writing this is the North Dallas .NET Users Group's first
kids night, where MinecraftU will be teaching the kids (and adults who stay
fo...